Displaying similar documents to “On the greatest prime factor of Markov pairs”

On the diophantine equation x - x = y - y.

Maurice Mignotte, Attila Petho (1999)

Publicacions Matemàtiques

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We consider the diophantine equation (*)    xp - x = yq - y in integers (x, p, y, q). We prove that for given p and q with 2 ≤ p < q, (*) has only finitely many solutions. Assuming the abc-conjecture we can prove that p and q are bounded. In the special case p = 2 and y a prime power we are able to solve (*) completely.

Diophantine equations with linear recurrences An overview of some recent progress

Umberto Zannier (2005)

Journal de Théorie des Nombres de Bordeaux

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We shall discuss some known problems concerning the arithmetic of linear recurrent sequences. After recalling briefly some longstanding questions and solutions concerning zeros, we shall focus on recent progress on the so-called “quotient problem” (resp. " d -th root problem"), which in short asks whether the integrality of the values of the quotient (resp. d -th root) of two (resp. one) linear recurrences implies that this quotient (resp. d -th root) is itself a recurrence. We shall also...

On the diophantine equation x 2 + 5 k 17 l = y n

István Pink, Zsolt Rábai (2011)

Communications in Mathematics

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Consider the equation in the title in unknown integers ( x , y , k , l , n ) with x ≥ 1 , y > 1 , n ≥ 3 , k ≥ 0 , l ≥ 0 and gcd ( x , y ) = 1 . Under the above conditions we give all solutions of the title equation (see Theorem 1).